The key assumption that leads to problems in trying to descriptively model people's decisions is just that people have a single consistent utility function, which is defined in terms of the amount of money that they have.
If someone starts with $18,000 and then gets $40, the assumption is that the benefit can be expressed as U(18,040)-U(18,000). Or, in words, the person thinks: getting $40 brought me from a world where I have $18,000 to a world where I have $18,040. I value a world where I have $18,000 at this amount, and I value a world where I have $18,040 at that amount, and the benefit of getting the $40 is just the difference between those two.
In this model, there is a single curve that you can plot of how much you value a world where you had $X. Think about what that curve would look like, with X ranging from 10,000 to 100,000. In nearly every plausible case, that curve will be close to linear on a small scale (in the range of 10s or 100s) almost everywhere. There may be some curvature to it (perhaps your curve resembles f(x)=log(x)), but if you zoom in then that will mostly go away and a straight line will give you a good fit (e.g., if you are looking at changes in x that are 2 orders of magnitude smaller than x, then a log function will look pretty much linear). In a few special cases, there may be a large sudden jump in the curve, if there is some specific thing that you really want to buy and there is a large benefit to suddenly being able to afford it, but those cases are rare. For the most part, U(x) will be relatively smooth, and it will be growing perceptibly over the whole range (even if your utility function is bounded, it's not like it will be almost at that bound before you even have $100,000).
And if your curve is approximately linear over small scales, then expected utility theory basically reduces to expected value theory when the stakes are small (e.g., a 50% of gaining $40 has an EV of $20). If U(x) is close to linear from x=18,000 to x=18,040, then U(18,020) must be about halfway in between U(18,000) and U(18,040). If you have $18,000, and are basing your decisions on a consistent utility function U(x), then for pretty much any plausible U(x) you'll prefer a 51% chance of gaining $40 to a 100% chance of gaining $20 (unless you just happen to have one of those rare big jumps in U(x) between $18,000 and $18,020 - perhaps you really really want something that costs $18,010?). The expected value is 2% higher ($20.40 vs. $20), and it's not plausible that your U(x) would be so sharply curved that you'd be willing to give up 2% EV over such a narrow range of x (it's just a 0.2% increase in x from $18,000 to $18,040).
Probably the most important feature of prospect theory is that it does away with this assumption of a single consistent utility function, and says that people value gambles based on the change from the status quo (or occasionally some other reference point, but we'll ignore that wrinkle here). So people think about the value of gaining $40 as U(+40) - it's whatever I have now plus forty dollars. The gamble in the previous paragraph now involves comparing U(+0), U(+20), and U(+40), rather than U(18,000), U(18,020), and U(18,040). It is no longer true that the scale of the change is small relative to the total amount, because the scale of the change sets the scale. So if there is any nonlinear curvature in your utility function, we can't get rid of it by zooming in to the point where we can use linear approximations, because no matter what we'll be looking at the function from U(+0) to U(+x). The utility function is at its curviest (least linear) near zero (think about log(x), or even sqrt(x)), and every change is defined relative to the status quo U(+0), so the curviest part of the curve is influencing every decision.
An assumption here that needs to be abandoned in order to have an accurate descriptive model of human decision making is that people have a single consistent utility function, which is defined in terms of the amount of money that they have.
That wasn't an assumption to be abandoned, that was the beginning of a proof by contradiction.
Expected utility maximalisation is an excellent prescriptive decision theory. It has all the nice properties that we want and need in a decision theory, and can be argued to be "the" ideal decision theory in some senses.
However, it is completely wrong as a descriptive theory of how humans behave. Those on this list are presumably aware of oddities like the Allais paradox. But we may retain some notions that expected utility still has some descriptive uses, such as modelling risk aversion. The story here is simple: each subsequent dollar gives less utility (the utility of money curve is concave), so people would need a premium to accept deals where they have a 50-50 chance of gaining or losing $100.
As a story or mental image, it's useful to have. As a formal model of human behaviour on small bets, it's spectacularly wrong. Matthew Rabin showed why. If people are consistently slightly risk averse on small bets and expected utility theory is approximately correct, then they have to be massively, stupidly risk averse on larger bets, in ways that are clearly unrealistic. Put simply, the small bets behaviour forces their utility to become far too concave.
For illustration, let's introduce Neville. Neville is risk averse. He will reject a single 50-50 deal where he gains $55 or loses $50. He might accept this deal if he were really rich enough, and felt rich - say if he had $20 000 in capital, he would accept the deal. I hope I'm not painting a completely unbelievable portrait of human behaviour here! And yet expected utility maximalisation then predicts that if Neville had fifteen thousand dollars ($15 000) in capital, he would reject a 50-50 bet that either lost him fifteen hundred dollars ($1 500), or gained him a hundred and fifty thousand dollars ($150 000) - a ratio of a hundred to one between gains and losses!
To see this, first define define the marginal utility at $X dollars (MU($X)) as Neville's utility gain from one extra dollar (in other words, MU($X) = U($(X+1)) - U($X)). Since Neville is risk averse, MU($X) ≥ MU($Y) whenever Y>X. Then we get the following theorem:
This theorem is a simple result of the fact that U($(X+55))-U($X) must be greater than 55*MU($(X+55)) (each dollar up from the Xth up to the (X+54)th must have marginal utility at least MU($(X+55))), while U($X)-U($(X-50)) must be less than 50*MU($(X-50)) (each dollar from the (X-50)th up to (X-1)th must have marginal utility at most MU($(X-50))). Since Neville rejects the deal, U($X) ≥ 1/2(U($(X+55)) + U($(X-50)), hence U($(X+55))-U($X) ≤ U($X)-U($(X-50)), hence 55*MU($(X+55)) ≤ 50*MU($(X-50)) and the result follows.
Hence if we scale Neville's utility so that MU($15000)=1, we know that MU($15105) ≤ 10/11, MU($15210) ≤ (10/11)2, MU($15315) ≤ (10/11)3, ... all the way up to to MU($19935) = MU($(15000 + 47*105)) ≤ (10/11)47. Summing the series of MU's from $15000 to $(15000+48*110) = $20040, we can see that
One immediate result of that is that Neville, on $15000, will reject a 50-50 chance of losing $1144 versus gaining $5000. But it gets much worse! Let's assume that the bet is a 50-50 bet which involves losing $1500 - how far up in the benefits do we need to go before Neville will accept this bet? Now the marginal utilities below $15000 are bounded below, just as those above $15000 are bounded above. So summing the series down to $(15000-1500) = $13500 > $(15000 - 14*105):
So gaining $5040 from $15000 will net Neville (at most) 1143 utilons, while losing $1500 will lose him (at least) 2937. The marginal utility for dollars above the 20040th is at most (10/11)47 < 0.012. So we need to add at least (2937-1143-1)/0.012 ≈ 149416 extra dollars before Neville would accept the bet. So, as was said,
These bounds are not sharp - the real situation is worse than that. So expected utility maximisation is not a flawed model of human risk aversion on small bets - it's a completely ridiculous model of human risk aversion on small bets. Other variants such as prospect theory perform a better job at the descriptive task, though as usual in the social sciences, they are flawed as well.